A268810 a(n) = 2*floor(3*n*(n+1)/4).

0, 2, 8, 18, 30, 44, 62, 84, 108, 134, 164, 198, 234, 272, 314, 360, 408, 458, 512, 570, 630, 692, 758, 828, 900, 974, 1052, 1134, 1218, 1304, 1394, 1488, 1584, 1682, 1784, 1890, 1998, 2108, 2222, 2340, 2460, 2582, 2708, 2838, 2970, 3104, 3242, 3384, 3528, 3674, 3824, 3978, 4134, 4292

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).

Formula

a(n) = (3*n^2 - 3*n + cos(n*Pi/2) + sin(n*Pi/2) - 1)/2.

a(n) = A268428(n) - 149.

a(n) = (1/4+i/4)*((i-1)+(-i)^n-i*i^n-(-3*i+3)*n+(-3*i+3)*n^2), where i is the imaginary unit.

a(n) = (3*n^2 - 3*n + (-1)^binomial(n+1,2) - 1)/2.

G.f.: (2*(x^3 + x^2 + x)/((1 - x)^3*(x^2 + 1))).

Mathematica

Table[2 Floor[3 n (n + 1)/4], {n, 0, 60}]
LinearRecurrence[{3, -4, 4, -3, 1}, {0, 2, 8, 18, 30}, 60]

Prog

(Magma) [2*Floor(3*n*(n+1)/4): n in [0..60]]; // Vincenzo Librandi, Feb 15 2016
(PARI) vector(60, n, n--; 2*floor(3*n*(n+1)/4)) \\ G. C. Greubel, Nov 04 2018

Crossrefs

Cf. A087960, A268428.

Sequence in context: A295522 A065131 A192157 * A063581 A293296 A055044

Adjacent sequences: A268807 A268808 A268809 * A268811 A268812 A268813

Keyword

nonn,easy

Author

Mikk Heidemaa, Feb 13 2016

Status

approved